D800 and Nikon SB-910 Speedlight.....Most of the time I'm shooting manual or aperture priority.

I'm aware that stepping down my exposure compensation will darken the background. Likewise I am aware that my flash exposure compensation will adjust the power of the flash itself preventing the flash from overexposing the subject. I guess I am mainly confused as to whether or not I need to mess with the exposure directly on the flash itself, or am I accomplishing the same thing by adjusting my flash exposure compensation in camera.

Yes, sure, you can adjust flash compensation on the camera.

Or, you can adjust flash compensation on the flash body (if it is on the hot shoe). They do the same thing.

If you do it BOTH places, they will add to a total that will be used. But you do not NEED to mess with that on the body, but you can.

Nikon (I think Canon is different) : Exposure Compensation affects both ambient and flash exposure. Flash Compensation affects only flash. So for example, if you set -2EV Exposure compensation, and +2 EV Flash compensation, then ambient will be reduced, and flash will be restored to 0 EV original state (the sum).

And Flash Compensation could be the sum of on camera FC, on flash FC, and also from Exposure Compensation, all sources added to a total. for the flash. So, it is good to standardize on one way, so you can keep up with what you did. If you see the =/- icon symbol in the viewfinder, you have some form of compensation on somewhere.

Fill flash in sunlight: What you need to know is this: TTL BL mode tries to do this balanced fill automatically, and it probably needs very little flash compensation. But TTL mode always tries to provide full metered flash exposure, and as fill flash in sunlight, you will surely want about -1.7EV Flash Compensation with TTL mode. Again, TTL BL mode tries to do that automatically. Big difference.